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Browsing by Subject "Stochastic partial differential equations"

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    Filtering partially observable diffusions up to the exit time from a domain.
    (2012-07) Wang, Teng
    We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary. We also derive a formula for the conditional distribution of the exit time if the observation is always available.